Yoneda structures from 2-toposes

Mark Weber

    Research output: Contribution to journalArticle

    22 Citations (Scopus)

    Abstract

    A 2-categorical generalisation of the notion of elementary topos is provided, and some of the properties of the Yoneda structure (Street and Walters, J. Algebra, 50:350–379, 1978) it generates are explored. Results enabling one to exhibit objects as cocomplete in the sense definable within a Yoneda structure are presented. Examples relevant to the globular approach to higher dimensional category theory are discussed. This paper also contains some expository material on the theory of fibrations internal to a finitely complete 2-category (Street, Lecture Notes in Math., 420:104–133, 1974) and provides a self-contained development of the necessary background material on Yoneda structures.
    Original languageEnglish
    Pages (from-to)259-323
    Number of pages65
    JournalApplied Categorical Structures
    Volume15
    Issue number3
    DOIs
    Publication statusPublished - 2007

    Keywords

    • 2-topos
    • fibration
    • Yoneda structure
    • internal category theory

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